TY  - EJOU
AU  - Chang, Chih-Wen  
AU  - Liu, Chein-Shan  

TI  - A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Advection-Dispersion Equation
T2  - Computers, Materials \& Continua

PY  - 2010
VL  - 17
IS  - 1
SN  - 1546-2226

AB  - In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is offered. The solver utilized in this work can retrieve the spatial distribution of the groundwater contaminant concentration. Several numerical examples are scrutinized to display that the new method can recover all the past data very well, and is good enough to deal with heterogeneous parameters, even though the final time data are noised seriously.
KW  - Groundwater contaminant distribution
KW  -  Backward advection-dispersion equation
KW  -  Fredholm integral equation
KW  -  Ill-posed problem
KW  -  Fourier series

DO  - 10.3970/cmc.2010.017.019